The present invention relates to a fiber optic gyro which allows light waves to pass clockwise and counterclockwise through a circular optical path of at least one loop, makes the light waves interfere with each other, and measures from the resulting interference light an angular velocity applied to the optical path.
FIG. 1 shows a conventional fiber optic gyro. Light 18 emitted from a light source 11 is provided via an optical coupler/splitter 12 and a polarizer 13 to an optical coupler/splitter 14, by which it is split into light waves 19 and 20 for propagation in opposite directions through a circular optical path 16 which makes at least one loop. A phase modulator 15 is connected in cascade between the optical coupler/splitter 14 and the optical path 16. The output of an oscillator 27 is provided via a phase modulator drive circuit 28 to the phase modulator 15, by which the light waves 19 and 20 are phase modulated. The light waves 19 and 20 having passed through the optical path 16 are applied as interference light 21 to a photodetector 17 via the optical coupler/splitter 12. The intensity I.sub.0 of the interference light 21 in this instance is given by the following equation (1): ##EQU1## In the above C is a constant, Jn(x) is an nth order Bessel function of the first kind, x is 2A sin .pi.f.sub.m .tau., where A is the amplitude of a light phase-modulating signal and .tau. is the time for the propagation of the light waves through the optical path 16, .omega. is the driving frequency of the phase modulator 15 (where .omega.=2.pi.f.sub.m), .DELTA..phi. is the phase difference between the light waves having propagated through the optical path 16 in opposite directions (where .DELTA..phi.=4.pi.RL.OMEGA./(c.lambda.), R being the radius of the optical path 16 L the length of the optical path 16, c the velocity of light, .lambda. the wavelength of light, and .OMEGA. an angular velocity applied to the optical path 16 in its circumferential direction), and .phi. is the phase difference between a drive voltage V.sub.pm applied to the phase modulator 15, V.sub.pm =A sin .omega..sub.t, and the phase-modulated light.
As is evident from Eq. (1), the intensity I.sub.o of the interference light 21 contains a term proportional to cos .DELTA..phi. and a term proportional to sin .DELTA..phi.. Since the interference light detecting sensitivity increases when the phase difference .DELTA..phi. is within a range of approximately .+-..pi./4 about each of .+-.m.pi. (where m=0, 1, 2, . . . ), the component proportional to sin .DELTA..phi. in the output of the photodetector 16 is detected by a synchronous detector 22. Setting a reference signal V.sub.r1a in the synchronous detector 22 as follows: ##EQU2## where .phi..sub.f is the phase difference between the drive voltage applied to the phase modulator 15, V.sub.pm =A sin .omega..sub.t, and the phase-modulated light, the output V.sub.1a of the synchronous detector 22 will become as follows: EQU V.sub.1a =K.sub.1 J.sub.1 (x) sin .DELTA..phi. cos (.theta.-.theta..sub.f)(3)
where K.sub.1 is a constant. Furthermore, since the interference detecting sensitivity increases when the phase difference .DELTA..phi. is within a range of approximately.+-..pi./4 about each of.+-.(2m+1).multidot..pi./2 (where m=0, 1, 2, . . . ), the component proportional to cos .DELTA..phi. in the output of the photodetector 17 is detected by a synchronous detector 23. Setting a reference signal V.sub.r2a in the synchronous detector 23 as follows: ##EQU3## the output V.sub.2a of the synchronous detector 23 will become as follows: EQU V.sub.2a =K.sub.2 J.sub.2 (x) cos .DELTA..phi. cos 2 (.theta.-.theta..sub.f)(5)
where K.sub.2 is a constant. The outputs of the synchronous detectors 22 and 23 are applied to low-pass filters 24 and 25, whose outputs V.sub.1a and V.sub.2a are provided to terminals 29 and 30, respectively. The output of the oscillator 27 is applied as the reference signal V.sub.r2a to the synchronous detector 23 and at the same time it is applied as the reference signal V.sub.1a to the synchronous detector 22 via a logic circuit 26.
To enlarge the dynamic range of the fiber optic gyro, the synchronous detector output V.sub.1a or V.sub.2a is derived as an output V.sub.0, depending on whether the phase difference .DELTA..phi. is in the range of.+-..pi./4 about.+-.m.pi. or.+-.(2m+1).pi./2 (where m= 0, 1, 2, . . . ), and the number of times of switching between the synchronous detector outputs V.sub.1a and V.sub.2a is measured, thereby obtaining angular velocity information .OMEGA..sub.i from the following equation (6): ##EQU4## where K[rad/v] is a conversion gain. That is, in FIG. 2 the component proportional to sin .DELTA..phi.(signal 72 in FIG. 3) and the component proportional to cos .DELTA..phi.(a signal 73 in FIG. 3) are applied to the terminals 29 and 30, respectively. The signal proportional to sin .DELTA..phi. and the signal proportional to cos .DELTA..phi. are switched therebetween in a switch 61 by an output D from that one of terminals of a reversible counter 70 which is weighted 2.sup.0. The output of the switch 61 is polarity inverted in a switch 62 by an output E from that one of the terminals of the reversible counter 70 which is weighted 2.sup.1, and the polarity-inverted output is provided to a gyro output terminal 65 via a linearizer 64. The output of the switch 62 is applied to a non-inverting input terminal and an inverting input terminal of comparators 66 and 67, respectively, wherein it is compared with reference voltages +V.sub.r and -V.sub.r of reference power supplies 68 and 69. The outputs of the comparators 66 and 67 are provided to up-and down-count terminals UP and DOWN of the reversible counter 70, in which they are counted up and down, respectively. The output D at the output terminal of the reversible counter 70, weighted 2.sup.0, is applied as a switching control signal to the switch 61, and the output E at the output terminal weighted 2.sup.1 is applied as a switching control signal to the switch 62. The switches 61 are each changed over to a terminal NC in the initial state (in which the switching control signal is as logic "0") and is altered to a terminal NO when the switching control signal is a logic "1". The count value of the reversible coutner 70 can be derived from a terminal 71.
As referred to previously, the output at the terminal 29 varies in proportion to sin .DELTA..phi. as shown by the curve 72 in row A of FIG. 3, while the output at the terminal 30 varies in proportion to cos .DELTA..phi. as shown by the curve 73 in row A of FIG. 3. When the phase difference .DELTA..phi. is in the range of.+-..pi./4, the switches 61 and 62 each remain in the state shown in FIG. 2 and the output from the terminal 29, which is proportional to sin .DELTA..phi., is linearized by the linearizer 64, thereafter being provided to the gyro output terminal 65. When the input to the comparator 66, i.e. the output from the switch 62 exceeds the reference voltage V.sub.r, pulses will be produced as shown in row B of FIG. 3. The pulses are additively counted by the reversible counter 70.
On the other hand, when the output of the switch 62 exceeds the reference voltage -V.sub.r in the negative direction, pulses will be created as shown in row C of FIG. 3 and subtractively counted by the reversible counter 70. The output D of the reversible counter 70, weighted 2.sup.0, varies as shown in row D of FIG. 3, and the output E weighted 2.sup.1 varies as shown in row E of FIG. 3. When the 2.sup.0 -weighted output D of the reversible counter 70 is high-level (logic "1"), the switch 61 is changed over and the signal at the terminal 30, that is, the output proportional to cos .DELTA..phi. is linearized and then provided to the gyro output terminal 65. Conversely, when the output of the switch 62 becomes larger than the reference voltage -V.sub.r in the negative direction, the comparator 67 yields pulses, which are subtractively counted by the reversible counter 70. In consequence, the 2.sup.0 -weighted output D goes high, by which the switch 61 is actuated and, as is the case with the above, the signal at the terminal 30, i.e. the output proportional to cos .DELTA..phi. is linearized and then provided to the gyro output terminal 65.
When the phase difference .DELTA..phi. increases in absolute value and the output proportional to cos .DELTA..phi. exceeds the reference voltage +V.sub.r or -V.sub.r in absolute value, pulses are produced from the comparators 66 and 67 and are additively or subtractively counted by the reversible counter 70, the switch 61 is returned to its initial position, and the signal 29, that is, the output proportional to sin .DELTA..phi. is linearized and provided to the gyro output terminal 65. At the same time, a signal polarity inversion command (a switching control signal) is provided by the 2.sup.1 -weighted output E of the reversible counter 70 so that the outputs proportional to sin .DELTA..phi. and cos .DELTA..phi. become positive relative to the phase difference .DELTA..phi., and the switch 62 is connected to an inverter 63. In the above, if the output voltages of the switch 62, which are proportional to sin .DELTA..phi. and cos .DELTA..phi. when the phase difference .DELTA..phi. is .pi./4, are set slightly lower than the reference voltages +V.sub.r and -V.sub.r in absolute value, then a sawtooth output can be obtained in the output terminal 65 as shown in row G of FIG. 3 and a hysteresis can be provided in the switching between the signals proportional to sin .DELTA..phi. and cos .DELTA..phi., ensuring a stable operation. In this way, when the phase difference .DELTA..phi. is in the range of around.+-..pi./4 about.+-.m.pi., the sin .DELTA..phi. component is provided as the gyro output and when the phase difference is in the range of around.+-..pi./4 about.+-.(2m+1) .pi./2, the cos .DELTA..phi. component is provided as the gyro output, by which the output can be obtained with a high degree of linearity throughout the entire range thereof. From this output the angular velocity can be obtained using Eq. (6). In Eq. (6) V.sub.0 is the voltage at the gyro output terminal 65 and m is the difference between the total numbers of pulses added and subtracted by the reversible counter 70, that is, the count value of the reversible counter 70, which is derived from the terminal 71.
For appropriate extraction of the sin .DELTA..phi. and cos .DELTA..phi. components from the photoelectric conversion output signal of the photodetector 17 it is necessary that the signal to be detected and the reference signal in each synchronous detector be substantially in phase with each other.
However, the phase difference .theta. between the drive voltage V.sub.pm which is applied to the phase modulator 15 and the fundamental frequency component of the interference light (the phase difference in the high-frequency component assumes a value multiplied by the harmonic order concerned as indicated by Eq. (1)) changes with the surrounding conditions, in particular, temperature to which the phase modulator 15 is exposed. Since the phase modulator 15 is made, for example, by winding an optical fiber around a cylindrical electrostrictive vibrator, its input/output phase chracteristic is essentially liable to vary with the surrounding conditions. In addition, when the operating point of the phase modulator 15 is set at its resonance point, the input/output phase characteristic becomes markedly variable with the surrounding conditions. Incidentally, the operating point of the phase modulator 15 is usually set at its resonance point. On this account, the signal to be detected and the reference signal in each of the synchronous detectors 22 and 23 are not in phase with each other, incurring variations in the scale factor of the outputs V.sub.1a and V.sub.2a as seen from Eqs. (3) and (5 ). This is nothing but a change in the gyro output V.sub.0, resulting in an error in the measurement of the angular velocity by the fiber optic gyro whose input range is intended to be enlarged, as will be seen from Eq. (6).
Conventionally the following method has been used to stabilize the scale factor. FIG. 4 illustrates a functional block diagram of a scale factor stabilizer circuit by which the amplitude K.sub.1 .multidot.J.sub.1 (x) of the output V.sub.1a in Eq. (3) is held constant. The output of the photodetector 17 is applied to synchronous detectors 31 and 32, in which synchronous detection is carried out at a phase modulating frequency f.sub.0 and a frequency 2f.sub.0 twice higher than the former, respectively. The outputs of the synchronous detectors 31 and 32 are squared by squaror circuits 33 and 34, respectively, and their square output V.sub.1.sup.2 and V.sub.2.sup.2 are added together by an adder 35, whose output voltage V becomes as follows: EQU V=V.sub.1.sup.2 +V.sub.2.sup.2 =(K.sub.1 .multidot.P.sub.0 .multidot.J.sub.1 (x)).sup.2 .multidot.sin.sup.2 .DELTA..phi.+(K.sub.2 .multidot.P.sub.0 .multidot.J.sub.2 (x)).sup.2 .multidot.cos.sup.2 .DELTA..phi. (7)
where K.sub.1 and K.sub.2 are constants (such as an amplification gain, a photoelectric conversion gain, a synchronous detection gain, etc.). Adjusting the total gain so that K.sub.1 .multidot.P.sub.0 .multidot.J.sub.1 (x)=K.sub.2 .multidot.P.sub.0 .multidot.J.sub.2 (x) and letting the amplitude in this instance be represented by K, the output voltage V becomes, from Eq. (7), as follows: EQU V=K.sup.2 .multidot.(sin.sup.2 .DELTA..phi.+cos.sup.2 .DELTA..phi.)=K.sup.2( 8)
Now, let the initial value or reference value of the output voltage V be represented by K.sub.R.sup.2. By detecting the difference between the reference value K.sub.R.sup.2 of a reference level generator 36 and the output voltage V with a differential amplifier 37 and negatively feeding back the difference to a light power control circuit 39 via an integrator 38, the amplitude of the output V.sub.1 can be maintained constant even if the power of light from the light source, an optical transmission loss and the polarized state of light vary.
This will be described in concrete terms. If a maximum power of light P.sub.0 arriving at the photodetector 17 is reduced by some cause and the voltage V drops below the reference value K.sub.R.sup.2 of the reference signal generator 36, the differential amplifier 37 will yield a positive signal. By setting the system with this positive signal so that the power of light which is emitted from the light source 11 increases, the maximum power of light P.sub.0 which reaches the photodetector 17 will increase. On the other hand, when the maximum power of light P.sub.0 increases by some cause and the voltage V exceeds the reference value K.sub.R.sup.2, the differential amplifier 37 yields a negative signal, decreasing the power of light which is emitted from the light source 11. As a result of this, the maximum power of light P.sub.0 which reaches the photodetector 17 will diminish. Thus, the voltage V can always be held at the reference value K.sub.R.sup.2. In other words, the amplitude of the output V.sub.1 can be retained constant.
The amplitude of the output V.sub.1 can similarly be maintained constant also by providing at the stage following the photodetector 17 a gain control circuit whose gain can be varied by an external signal and by a negative feedback thereto the output of the integrator 38.
With the conventional scale factor stabilizer circuit it is necessary, for ensuring stabilization of the scale factor, that the x which is a variable of the Bessel functions of the first kind, J.sub.1 (x) and J.sub.2 (x), be highly stable. Even if a method for stabilizing the value x is employed, a control error occurs and the value x varies, though slightly. Normally the value x is set to 1.84 at which the output V.sub.1 is detected with a maximum sensitivity. With x=1.84, J.sub.1 (x) is stable regardless of a change in the value x but J.sub.2 (x) which is a coefficient of the output V.sub.2 is not stable and readily varies with a change in the value x, as shown in FIG. 5. When the value x undergoes such a change, K.sub.1 .multidot.P.sub.0 .multidot.J.sub.1 (x).noteq.K.sub.2 .multidot.P.sub.0 .multidot.J.sub.2 (x) and Eq. (8) does not hold. In other words, the scale factor stabilizer circuit will not normally operate and the scale factor as the input/output characteristic of the fiber optic gyro cannot be held highly stable.
In FIG. 4 reference signals of frequencies f.sub.0, 3f.sub.0 and 2f.sub.0 are supplied from a reference signal generator 41 to the synchronous detectors 31, 42 and 32, which yield signals V.sub.1, V.sub.3 and V.sub.2, respectively. Since signals V.sub.1 and V.sub.3 may assume both positive and negative voltages according to positive and negative input angular velocities which are applied to the optical path 16, they are converted by absolute circuits 43 and 44 into absolute values. The absolute circuits 43 and 44 may be replaced by squaror circuits. The output of the absolute circuit 43 is applied to a plus (+) input of a differential amplifier 45 and the output of the absolute circuit 44 is applied to a minus (-) input of the differential amplifier 45.
The output of the differential amplifier 45 is provided via an integrator 46 to the phase modulator drive circuit 28. The phase modulator drive circuit 28 has an arrangement in which the voltage of the signal of the driving frequency f.sub.0, which is applied to the phase modulator 15, is increased and decreased by a positive and a negative signal from the differential amplifier 45, respectively. Thus an automatic control loop is provided.
With such an arrangement, when the output of the differential amplifier 45 is zero, that is, when V.sub.1 =V.sub.3 (let it be assumed, in this case, that the constants K.sub.1 and K.sub.3 have been preadjusted to be equal to each other), the voltage which is applied to the phase modulator 15 is adjusted by the phase modulator drive circuit 28 so that the Bessel functions of the first kind J.sub.1 (x) and J.sub.3 (x) assume the same value, i.e. about 3.05 in terms of the value x at the point A in FIG. 5.
Provided that the amplitude A of the phase modulating signal increases and consequently the value x increases, the Bessel function J.sub.1 (x) increases but J.sub.3 (x) decreases as indicated at the point A in FIG. 5. As a result of this, the differential amplifier 45 applies a negative signal to the integrator 46, the output of which decreases and the phase modulator drive circuit 28 decreases the voltage of a drive signal to be applied to the phase modulator 15 accordingly, thus causing a decrease in the value of the amplitude A of the phase modulating signal.
On the other hand, in the case where the amplitude A of the phase modulating signal decreases and the value x decreases correspondingly, the first order Bessel function J.sub.1 (x) increases but the third order Bessel function J.sub.3 (x) decreases as shown in FIG. 5. In consequence, the differential amplifier 45 applies a positive signal to the integrator 46. The integrator 46 increases its output and the phase modulator drive circuit 28 increases the voltage of the drive signal to be applied to the phase modulator accordingly, thus increasing the value of the amplitude A of the phase modulating signal.
In this way, the value x and consequently the sensitivity as the gyro output can be held constant at all times, even if the amplitude A of the phase modulating signal is changed by surrounding conditions or external forces which are applied to the device. The integrator 46 disposed between the differential amplifier 45 and the phase modulator drive circuit 28 is to eliminate a residual deviation of the differential amplifier 45 in the proportional action, thereby maintaining the value x at a target value (x=3.05) at all times.
As mentioned previously, the prior art employs the outputs V.sub.1 and V.sub.3 of the synchronous detectors 31 and 42 as control signals for stabilization of the phase modulation. The outputs V.sub.1 and V.sub.3 are expressed by the following equations: EQU V.sub.1 =K.sub.1 .multidot.P.sub.0 .multidot.J.sub.1 (x) sin .DELTA..phi.(9) EQU V.sub.3 =K.sub.3 .multidot.P.sub.0 .multidot.J.sub.3 (x) sin .DELTA..phi.(10)
The outputs V.sub.1 and V.sub.3 are in proportion to sin .DELTA..phi.. Therefore, when the input angular velocity is zero or extremely small, the outputs are zero or extremely small, making it impossible to effect control for stabilizing the phase modulation. In this instance, the integrator 46 is positively or negatively saturated and the amplitude of the phase modulating signal becomes maximum or minimum. In such a state the gyro cannot respond to a high-speed input, and hence cannot be expected to perform a normal operation for stabilizing the phase modulation and the scale factor.